Least Common Multiple (LCM) of 78 and 31
The least common multiple (LCM) of 78 and 31 is 2418.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 78 and 31?
First, calculate the GCD of 78 and 31 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 31 = 2 remainder 16 |
| 2 | 31 ÷ 16 = 1 remainder 15 |
| 3 | 16 ÷ 15 = 1 remainder 1 |
| 4 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 197 | 20685 |
| 132 and 12 | 132 |
| 71 and 99 | 7029 |
| 120 and 162 | 3240 |
| 170 and 43 | 7310 |